A reaction-distillation apparatus is provided comprising at least one reaction-distillation zone including at least one bed of solid elements disposed on a fluid-permeable perforated support having perforations small enough to retain the elements wherein the bed of solid elements includes loose solid catalytic particles and at least one receptacle, containing at least one distillation packing body, the external jacket of which is permeable to fluids and the impermeable to the solid catalytic particles and packing body. The apparatus can be used for carrying out chemical reaction and concomitant fractionation of the reaction mixture, for example, to synthesize ethers from olefins and alcohols.